Genova, September 1 2004

Routes to Colloidal Gel Formation

CCP2004

In collaboration with S. Bulderyev, E. La Nave, A. Moreno, S. Mossa, I. Saika-Voivod, P. Tartaglia, E. Zaccarelli

Thanks to the organizers and to Carlo Pierleone

Outline and Motivations

Brief Review of Short-Range Attractive Colloidal Glass (asymmetric colloid-polymer mixtures)

How to model disordered arrested states at low packing fraction (gels)

Routes: Interrupted phase separation (irreversible gels) Long Range Repulsive interactions (reversible) Geometrical constraints (reversible)

Differences between gel and glasses

Depletion Interactions:A (C. Likos) Cartoon

V(r )

r

MCT IDEAL GLASS LINES (PY) - SQUARE WELL MODEL - CHANGING

PRE-63-011401-2001

A4

V(r)

A3

Large Small

F. Sciortino, Nat. Mat. 1, 145 (2002).

confirmed by experiments Mallamace et al. PRL (2000)

Pham et al. Science (2002) Eckert and Bartsch PRL (2002)

and simulations Puertas et al PRL (2002)Zaccarelli et al PRE (2002)

Pham et al 2004

Phase Diagram for Square Well (3%)

RepulsiveGlass

AttractiveGlassLiquid+Gas Coexistence

A3

Spinodal AHS (Miller&Frenkel)

Iso-diffusivity

lines

Percolation Line

Spinodal (and Baxter)

Virial Scaling in the dynamics:

Toward the Baxter Limit

G. Foffi and C. De Michele,preprint

Gelation as a result of phase separation

(interrupted by the glass transition)

T T

The quest for the ideal (thermoreversible) gel….model1) Long Living reversible bonds

2)No Phase Separation3) No Crystallization

Are 1 and 2 mutually exclusive ?LowTemperatur

e

Condensation

Long Bond Lifetime

Surface Tension

How to stay at low T without condensation ?

Reasons for condensation (Frank, Hill, Coniglio)

Physical Clusters at low T

if the infinite cluster is the lowest (free)energy state

How to make the surface as stable as the bulk (or more)?

Short Range Attraction

Long Range Repulsion

Competition Between Short Range Attraction and Long Range Repulsion

FS et al, PRL 2004

Groenewold

and Kegel

Upper Limit

Optimal Size

How to make negative ?

lowering T

Increasing packing fraction

Geometric Constraint: Maximum Valency

SW if # of bonded particles <= Nmax

HS if # of bonded particles > Nmax

V(r)

r

Phase Diagram

Bond Lifetime.. Several more decades..

Gel vs Glass - MSD

T=0.1

Typical Glass Value

Gel vs Glass: Density Autocorrelation Functions

fq

Fq gel vs glass

Summary….

• Designig Thermoreversible Gels: •Models with small surface tension (charged colloids, sticky points)

• A simple model for thermoreversible gel

• Gels and Glasses:•Differences in localization length •Differences in experimental observables

Ground State Energy Known !

It is possible to equilibrate at low T !

How to stay at low T without condensation ?

Reasons for condensation (Frank, Hill, Coniglio)

Physical Clusters at low T

if the infinite cluster is the lowest energy state

How to make the surface more stable than the bulk ?

Thermodynamics in the IS formalism Stillinger-Weber

F(T)=-T Sconf(<eIS>, T) +fbasin(<eIS>,T)

with

fbasin(eIS,T)= eIS+fvib(eIS,T)and

Sconf(T)=kBln[(<eIS>)]

Basin depth and shape

Number of explored basins

Free energy

It is possible to calculate exactly the basin free energy !

Viscosity and Diffusivity: Arrhenius

Stoke-Einstein Relation